Question

После строительства дома осталось некоторое количество плиток .их можно использовать для выкладывания прямоугольной площадки на участке рядом с домом .Если укладывать по 10плиток то для квадратной площадки плиток нехватает . при укладывании по 7 плиток в ряд остоется один неполный ряд а при укладывания по 8 тоже остоется неполный ряд в котором на 5 плиток меньше чем в неполном ряду при укладыванию по 7 . сколько всего плиток осталось после строительства дома ? Запишите решение и ответ

Answer 1

5*7=35 +6   -   41

5*8= 40+1   -   41

6-1=5

Осталась  41  плитка

Answer 2

Problem Analysis

The problem states that after constructing a house, there are some leftover tiles. These tiles can be used to create a rectangular platform next to the house. The problem provides information about the number of tiles required to create a square platform and the number of tiles left when arranging them in rows of 7 or 8. We need to determine the total number of tiles left after constructing the house.

Solution

Let's break down the information provided in the problem:

- When arranging the tiles in rows of 10, there are not enough tiles to create a square platform. - When arranging the tiles in rows of 7, there is one incomplete row left. - When arranging the tiles in rows of 8, there is also one incomplete row left, which is 5 tiles shorter than the incomplete row when arranging them in rows of 7.

To find the total number of tiles left, we need to determine the number of tiles in the incomplete rows when arranging them in rows of 7 and 8.

Let's denote the number of tiles in the incomplete row when arranging them in rows of 7 as x. According to the problem, the incomplete row when arranging them in rows of 8 is 5 tiles shorter than the incomplete row when arranging them in rows of 7. Therefore, the number of tiles in the incomplete row when arranging them in rows of 8 is x - 5.

To find the total number of tiles left, we need to calculate the sum of the number of tiles in the incomplete rows when arranging them in rows of 7 and 8, and add the number of tiles required to create a square platform.

Let's denote the total number of tiles left as T. We can express T as follows:

T = (x + (x - 5)) + 10^2

Now, we need to solve the equation to find the value of T.

Solution Steps

1. Calculate the value of x by solving the equation (x + (x - 5)) = 7^2. 2. Substitute the value of x into the equation T = (x + (x - 5)) + 10^2 to find the total number of tiles left.

Solution

Let's solve the equation to find the value of x:

(x + (x - 5)) = 7^2

Simplifying the equation:

2x - 5 = 49

Adding 5 to both sides:

2x = 54

Dividing both sides by 2:

x = 27

Now, substitute the value of x into the equation T = (x + (x - 5)) + 10^2:

T = (27 + (27 - 5)) + 10^2

Simplifying the equation:

T = (27 + 22) + 100

T = 49 + 100

T = 149

Therefore, the total number of tiles left after constructing the house is 149.

Answer

The total number of tiles left after constructing the house is 149.